Hamilton-Jacobi-Bellman Equation for Control Systems with Friction
Optimization and Control
2020-12-02 v3 Dynamical Systems
Abstract
This paper proposes a new framework to model control systems in which a dynamic friction occurs. The model consists in a controlled differential inclusion with a discontinuous right hand side, which still preserves existence and uniqueness of the solution for each given input function . Under general hypotheses, we are able to derive the Hamilton-Jacobi-Bellman equation for the related free time optimal control problem and to characterise the value function as the unique, locally Lipschitz continuous viscosity solution.
Cite
@article{arxiv.1909.08380,
title = {Hamilton-Jacobi-Bellman Equation for Control Systems with Friction},
author = {Fabio Tedone and Michele Palladino},
journal= {arXiv preprint arXiv:1909.08380},
year = {2020}
}